engleski

On the comparison of two different one-parametric generalizations of the logarithmic mean

There exist several generalizations of the well-known logarithmic mean. R. Cisbani, L. Galvani and E. L. Dod independently defined the extended logarithmic mean L_r. For certain r, this mean becomes the arithmetic mean, geometric mean, logarithmic mean and identric mean, but there is no such r for which it becomes harmonic mean. On the other hand, H. Alzer defined another one-parametric generalization - the generalized logarithmic mean F_r. For certain r, this mean becomes the arithmetic mean, geometric mean, harmonic mean and logarithmic mean, but there is no such r for which it becomes identric mean. In this talk, it is explained weather these two one-parametric generalizations of the logarithmic mean are comparable, and how. Their comparison with the power means is also given.

logarithmic mean ; extended logarithmic mean ; generalized logarithmic mean ; power mean

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